The amplitude instability without the GVD effect exhibits as that of an RNGH-type instability. From Fig. 1, it can be found that, under each pumping level, the presence of the GVD alters the influence of the saturable absorber on the amplitude instability. That is, an increase in the saturable absorber strength can drive the amplitude to be more stable when the GVD is present. Inversely, a stronger saturable absorber boosts the instability by lowering the instability threshold when the GVD is absent.10,12 Thus, the lasing cavity with a stronger saturable absorber effect is less affected by the presence of the GVD. The interaction between the GVD and the saturable absorber on the amplitude instability is also affected by the pumping strength . Figure 1(a) tells that, under low pumping strength, the GVD tends to destabilize the amplitude and flattens the parametric gain curve throughout all frequency modes. When the pumping strength gets stronger, as shown in Figs. 1(b), 1(c), and 1(d), the effect of the GVD can be suppressed by the saturable absorber effect. Hence, the instability without the GVD resembles that of the instability with the GVD, especially for the frequency portion that is closely around the central frequency. Apparently, to achieve such suppression, the weaker the saturable absorber is, the higher is the pumping strength needed. This is because of the fact that the suppression is related to the nonlinear portion of the loss . We notice that, in Figs. 1(c) and 1(d), for the case with the highest saturable absorber strength under study, the symmetry of the gain spectrum about the central frequency is broken, which is mathematically caused by the emergence of an imaginary part in the steady-state solution.